NumPy: convert decimals to fractions

Question

I compute the reverse of matrix A, for instance,

import numpy as np

A = np.diag([1, 2, 3])
A_inv = np.linalg.pinv(A)
print(A_inv)

I got,

[[ 1.          0.          0.        ]
 [ 0.          0.5         0.        ]
 [ 0.          0.          0.33333333]]

But, I want this,

[[ 1.          0.          0. ]
 [ 0.          1/2         0. ]
 [ 0.          0.          1/3]]

I tried np.set_printoptions,

import fractions
np.set_printoptions(formatter={'all':lambda x: str(fractions.Fraction(x))})
print(A_inv)

but I got this,

[[1 0 0]
 [0 1/2 0]
 [0 0 6004799503160661/18014398509481984]]

How do I convert decimals to fractions in NumPy?

Teplica

Are you just talking about the representation when printing it? Or do you actually want numpy to invert the matrix using something like fractions.Fraction? – Evenson

@mgilson, just for print purpose. – Teplica

you are running into floating point issues, try something like lambda x: str(fractions.Fraction(x).limit_denominator()) – Virgilvirgilia

@jeremycg, it works:-) – Teplica

Answer 1

This is a floating point issue - recall that 2/3 is not exactly 2/3 in Pythons representation.

The Fraction class has a built in method, limit_denominator(), to take care of this:

import fractions
np.set_printoptions(formatter={'all':lambda x: str(fractions.Fraction(x).limit_denominator())})
print(A_inv)

Which gives the desired answer:

[[1 0 0]
 [0 1/2 0]
 [0 0 1/3]]

Virgilvirgilia

Be aware that limit_denominator is doing something very specific, namely finding the closest rational approximation with denominator not exceeding 1 million. That may or may not be appropriate, depending on the use-case. In particular, it's not going to give particularly good results for very large or very small numbers. – Whereof

Many thanks. Do you have any idea to format print each elements into fixed width? I used np.set_printoptions(formatter={'str_kind': '{10s}'.format}, but didn't work. – Teplica

how to use a comma as separator instead of spaces – Gaekwar